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Ewan D. Barr edited scattering part2.tex
over 8 years ago
Commit id: 075c303d32470560263aa5354af9a9e9e715aed4
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\begin{equation}
\log_{10} \tau_s = -9.46 + 0.154 \log_{10} {\rm DM}+ 1.07 (\log_{10} {\rm DM})^2 - 3.86 \log_{10}{\nu}.
\end{equation}
where $\tau_s$ is the scattering time in seconds and $\nu$ is the observing frequency in GHz. The scatter of measured values about this relation ship has a standard deviation of several orders of magnitude. In the remainder of this document we take a conservative approach and assume scattering times 4 orders of magnitude smaller than those suggested by the above relation, i.e. the best-case scattering. As we will see, this approach results in reasonable requirements on the SKA1 pulsar timing instrumentation.
\begin{equation}
\log_{10} \tau_s_{\rm best} = -13.46 + 0.154 \log_{10} {\rm DM}+ 1.07 (\log_{10} {\rm DM})^2 - 3.86 \log_{10}{\nu}.
\end{equation}